Further results on -perfect difference families

In this paper, it is shown that an ASP ( 2 r + 1 , 3 ) exists for 2 ≤ r ≤ 100 and r ≠ 4 , 5 . The existence of a ( v , 4 , 1 ) -PDF is investigated by taking advantage of the relationship between ASPs and perfect difference families (PDFs). It is proved that a ( 12 t + 1 , 4 , 1 ) -PDF exists for t ≤ 100 and t ≠ 2 , 3 . Several recursive constructions for ASPs and PDFs are also presented. As a consequence, the existence results of an optimal ( v , 4 , 1 ) -OOC is updated.